Many real world systems, e.g., internet, World Wide Web (WWW), social systems, biological systems, etc., can be described as complex networks, which are structured as a set of nodes and a set of edges connecting the nodes. Scale-free network is the most popular and emerging form of network in these real world network systems. Most of these real world networks have been proved to follow some topological statistical features, i.e., features of scale-free network, such as power law degree distribution, small world property, and high modularity. Power law degree distribution depicts the probability of finding a highly connected node decreases exponentially with its own degree, which is the number of edges incident on the node. In other words, there are many low degree nodes, and only a small number of nodes have high degree. The second phenomenon, small world property, describes that the average distance between nodes in a network is relatively shorter than other network types, e.g., random networks of the same size. Namely, any node can be reached within small number of consecutive edges from a node in a network. A module refers to a densely connected, functionally or physically, group of nodes in a network. For the last distinct and the most interesting property, these real world networks have high modularity which indicates that high clustering is one of dominating characteristics of these networks.
Over the past few years, empirical and theoretical studies of networks have been one of the most popular subjects of recent research in many areas including technological, social, and biological fields. Network theories have been applied with good success to these real world systems, and many centrality indices, measurements of the importance of the components in a network, have been introduced. While these centrality indices have proved that they made outstanding achievements in the analysis and understanding of the roles of nodes in a network, the majority of these existing centrality indices focus only on the extent how much nodes are well located on central positions or play central roles from the stand point of topology and information flow. These existing centrality measures can not help being considerably dominated by the nodes' degree due to their nature of the computing components' importance. Even though these approaches are very good at identifying central components, i.e., central components from any centrality viewpoint, of a network or of a module, they concentrate only on central components and overlook other essential topological aspects in networks.
In this research, the focus of the network analysis is moved from the directions of identifying central nodes to another entirely new, fresh, and important direction. From our deeper observation of the high modularity property of scale free networks, we claim that there should be “bridging” nodes that are located between modules, and we found that there exist “bridging” nodes in real world scale-free networks due to their high modularity phenomenon. So, we also claim that these bridging nodes, which bridge densely connected regions, should be attractive and important essential components in a network. We introduce a novel centrality metric, bridging centrality that successfully identifies the bridging nodes located between densely connected regions, i.e., modules, using a high modularity or high clustering property which is one of the most important properties of scale-free networks. Experiments on several real world network systems are performed to demonstrate the effectiveness of our metric.
Bridging centrality has many potential applications in several areas. First, it can be used to break up modules in a network for clustering purpose. Functional modules or physical modules in biological networks or sub community structures in social and technological networks can be detected using the bridging nodes chosen by bridging centrality. Second, it also can be used to identify the most critical points interrupting the information flow in a network for network protection and robustness improvement purposes for networks. Third, in biological applications, the bridging centrality can be used to locate key proteins, which are the connecting nodes among functional modules.